A familiar result

Probability Level 3

$\large \dbinom{n}{r} \quad , \quad \dbinom{n}{r+1} \quad , \quad \dbinom{n}{r+2} \quad$

For some integers $n>r>0$ , the values of the three binomial coefficients above are all palindromes with more than one digit. Find the minimum possible value of $n+r$ .

Note: These numbers are written in decimal representations.

Image Credit: Wikimedia TED-43 .

The answer is 18.

1 solution

Nicole Tay
Feb 8, 2016

We can use Pascal's Triangle for an easier way for solving the problem. To find $\dbinom{n}{r}, \dbinom{n}{r+1}, \dbinom{n}{r+2}$ , look for three palindromes placed next to each other in a row of the triangle. Observe that 1001, 2002, and 3003 are next to each other and we are done. $\dbinom{14}{4}$ gives 1001, and 14+4=18.

A familiar result

Image Credit: Wikimedia TED-43 .

The answer is 18.

1 solution

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